Feedback regulation of proliferation vs. differentiation rates explains the dependence of CD4 T-cell expansion on precursor number

Gennady Bocharov*, Juan Quiel, Tatyana Luzyanina, Hagit Alon, Egor Chiglintsev, Valery Chereshnev, Martin Meier-Schellersheim, William E. Paul, Zvi Grossman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The mechanisms regulating clonal expansion and contraction of T cells in response to immunization remain to be identified. A recent study established that there was a log-linear relation between CD4 T-cell precursor number (PN) and factor of expansion (FE), with a slope of ∼-0.5 over a range of 3-30,000 precursors per mouse. The results suggested inhibition of precursor expansion either by competition for specific antigen-presenting cells or by the action of other antigen-specific cells in the same microenvironment as the most likely explanation. Several molecular mechanisms potentially accounting for such inhibition were examined and rejected. Here we adopt a previously proposed concept, "feedback-regulated balance of growth and differentiation," and show that it can explain the observed findings. We assume that the most differentiated effectors (or memory cells) limit the growth of less differentiated effectors, locally, by increasing the rate of differentiation of the latter cells in a dose-dependent manner. Consequently, expansion is blocked and reversed after a delay that depends on initial PN, accounting for the dependence of the peak of the response on that number. We present a parsimonious mathematical model capable of reproducing immunization response kinetics. Model definition is achieved in part by requiring consistency with available BrdU-labeling and carboxyfluorescein diacetate succinimidyl ester (CFSE)-dilution data. The calibrated model correctly predicts FE as a function of PN. We conclude that feedback-regulated balance of growth and differentiation, although awaiting definite experimental characterization of the hypothetical cells and molecules involved in regulation, can explain the kinetics of CD4 T-cell responses to antigenic stimulation.

Original languageEnglish
Pages (from-to)3318-3323
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number8
StatePublished - 22 Feb 2011


  • Parameter estimation
  • Time delay


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